Document Sample

A&A 488, 375–381 (2008) Astronomy DOI: 10.1051/0004-6361:200809894 & c ESO 2008 Astrophysics Speckle interferometry with adaptive optics corrected solar data F. Wöger1 , O. von der Lühe2 , and K. Reardon1 ,3 1 National Solar Observatory, PO Box 62, Sunspot, NM 88349, USA e-mail: fwoeger@nso.edu 2 Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, 79104 Freiburg, Germany 3 INAF – Osservatorio Astrosico di Arcetri, 50125 Firenze, Italy Received 2 April 2008 / Accepted 17 May 2008 ABSTRACT Context. Adaptive optics systems are used on several advanced solar telescopes to enhance the spatial resolution of the recorded data. In all cases, the correction remains only partial, requiring post-facto image reconstruction techniques such as speckle interferometry to achieve consistent, near-diﬀraction limited resolution. Aims. This study investigates the reconstruction properties of the Kiepenheuer-Institut Speckle Interferometry Package (KISIP) code, with focus on its phase reconstruction capabilities and photometric accuracy. In addition, we analyze its suitability for real-time re- construction. Methods. We evaluate the KISIP program with respect to its scalability and the convergence of the implemented algorithms with dependence on several parameters, such as atmospheric conditions. To test the photometric accuracy of the ﬁnal reconstruction, com- parisons are made between simultaneous observations of the Sun using the ground-based Dunn Solar Telescope and the space-based Hinode/SOT telescope. Results. The analysis shows that near real-time image reconstruction with high photometric accuracy of ground-based solar observa- tions is possible, even for observations in which an adaptive optics system was utilized to obtain the speckle data. Key words. techniques: high angular resolution – techniques: image processing – techniques: interferometric – sun: photosphere 1. Introduction the data amount is reduced by a factor of around 100. Thus, the possibility of real-time data reduction becomes attractive when Adaptive optics (AO) systems have been introduced to many post-processing techniques like speckle interferometry are con- solar telescopes in the recent years, making large aperture fa- sidered for image reconstruction. Some of the aspects of the ap- cilities feasible. However, it is evident that any AO correction plication of post-processing algorithms to speckle data in near is only partial. Thus, to achieve diﬀraction limited performance real-time have already been explored by Denker et al. (2001). of the telescope, further post-processing of the observations be- In this article, we present the characteristics of the comes necessary. Several algorithms for image reconstruction Kiepenheuer-Institut Speckle Interferometry Package (KISIP, have evolved as computational power has increased rapidly. On von der Lühe 1993; Mikurda & von der Lühe 2006), which has the one hand, techniques based on blind deconvolution like mul- been rewritten in the C programming language and enhanced tiframe blind deconvolution or the even more general multi- for parallel processing1. In Sect. 2, we give an overview of the object multiframe blind deconvolution have evolved and be- implemented algorithms. Section 3 describes our study of the come popular in the recent years (van Noort et al. 2005). On performance of the two implemented phase reconstruction al- the other hand, techniques based on speckle interferometry that gorithms, as well as the overall scalability of the code with an have evolved since the mid-1970s have been reﬁned and im- increasing number of computational nodes. In addition, the pho- proved (Labeyrie 1970; Knox & Thompson 1974; Weigelt 1979; tometric accuracy of the ﬁnal reconstruction is tested with both a Lohmann et al. 1983) during the 1980s. ground- and space-based telescope co-temporally observing the The rapid development of computer technology, especially same target on the Sun. in the ﬁeld of multi-core processors, makes a real-time appli- cation of reconstruction algorithms to speckle interferometric data feasible and warrants further development. The need for 2. Algorithmic details real-time – or at least near real-time – processing is clear when considering that speckle data is observed at high data rates: In this section, we brieﬂy describe the internal details of how in general, a single “speckle burst” consists of approximately KISIP was implemented to allow for parallel processing as well 100 images observed at a frame rate of around 15 images per sec- as the employed algorithms used for the reconstruction of the ond (or higher). When observing several hours a day this leads Fourier phase and amplitude. to a data volume of several hundred gigabytes of unreduced data In general, the imaging process through atmosphere and per day. Even though the cost per byte is continually decreasing, telescope is best described in the Fourier domain. Using the the handling (transfer and distribution) is a costly and lengthy process. Thus, the reduction of speckle data at the telescope site 1 The full C sources of the package are available at https://forge. is an important step to increase the telescope’s eﬃciency because kis.uni-freiburg.de/kisip Article published by EDP Sciences 376 F. Wöger et al.: Speckle interferometry with adaptive optics corrected solar data incoherent, space-invariant imaging equation, we get for a speckle burst consisting of N images Ii ( f ) = O( f ) Si ( f ), 1 ≤ i ≤ N, (1) where f is the two-dimensional, spatial frequency and Ii ( f ) is the Fourier transform of the ith observed image of the object de- scribed by O( f ). The term Si ( f ) is the ith transfer function that incorporates aberrations due to both atmosphere and telescope, and is generally a complex function. We assume that there are no static aberrations in the telescope, thus complex contribu- tions to the transfer function only arise from phase distortions due to Earth’s turbulent atmosphere. This is justiﬁed by the fact that most solar telescopes today use AO systems. These systems are capable to correct some of the atmospheric aberrations in Fig. 1. Time used for one reconstruction versus numbers of computation real-time, and additionally remove most of the static aberrations nodes used. Either 212992 cross-spectrum (KT) or 221320 bispectrum eﬃciently. (IWLS) values for averaging. At an early stage of the reconstruction process, each recorded short-exposed frame is split into subframes that have roughly the size as the isoplanatic patch (the area in the ﬁeld of view for The other algorithm available within the package is a speckle which the optical transfer function is considered constant) and masking (or triple correlation) algorithm. Speckle masking al- that overlap by half of their size. This makes a parallel treatment gorithms, the generalization of Knox and Thompson’s idea us- of the subframes easy as they are sent to separate computation ing the bispectrum, have been used since Weigelt (1979) and nodes using the message passing interface (MPI Forum 1997). Lohmann et al. (1983). The bispectrum is deﬁned as The KISIP package separates the image’s Fourier phases from its B(u, u) = Ii (u) Ii (u) Ii∗ (u + u) i amplitudes. The Fourier phases are treated with unity amplitude = Oi (u) Oi (u) O∗ (u + u) i (4) by both of the implemented phase reconstruction algorithms, × S i (u) S i (u) S i∗ (u + u) i . which are described in further detail below. Fourier amplitudes are reconstructed independently. In what follows, we give a brief In analogy to Eq. (3), it can be shown that the speckle masking overview over these well-known techniques that form the basis transfer function of KISIP. S MT F( f ) = S i (u) S i (u) S i∗ (u + u) (5) i is a real valued entity and remains ﬁnite up to the diﬀraction 2.1. Phase reconstruction limit (von der Lühe 1985). The rather stringent restriction for The KISIP program incorporates two diﬀerent algorithms to δ’s magnitude in the extended KT approach is relaxed for u and reconstruct the object’s Fourier phases. u from the seeing to the diﬀraction limit. The algorithm imple- In one case, the package uses an extension of the Knox- mented in KISIP is based on a technique described by Matson Thompson (KT) algorithm (Knox & Thompson 1974) which is (1991), who proposes the reconstruction of phases using an iter- based on the original authors’ idea to use average cross-spectra ative weighted least-squares (IWLS) ﬁt to the bispectrum. Thus, for the reconstruction of the object’s Fourier phases. The Knox- it makes full use of the bispectrum that was computed with user Thompson average cross-spectrum is deﬁned as speciﬁed truncation parameters to restrict it to a manageable size (e.g., Pehlemann & von der Lühe 1989). C( f , δ) = Ii ( f ) Ii∗ ( f − δ) i As the extended KT algorithm uses cross-spectra, i.e. mul- (2) = O( f ) O∗ ( f − δ) S i ( f ) S i∗ ( f − δ) i . tiplications of two Fourier phase values (see Eq. (2)), it is com- putationally less expensive than a speckle masking algorithm, Here, · i is the average over the N observed subframe images which involves the product of three phase values (Eq. (4)). It has that incorporate independent realizations of atmospheric distor- been shown that both implemented algorithms can be equivalent tions. The two-dimensional, spatial frequency shift vector δ can (Ayers et al. 1988). However, the Knox-Thompson algorithm have a magnitude of up to the seeing limit in the Fourier do- is sensitive to alignment errors of the speckle images, whereas main, r0 /λ, where λ denotes the observed wavelength and r0 is triple correlation algorithms do not suﬀer from this because of the Fried parameter describing the prevailing atmospheric con- the phase closure relation inherent to the bispectrum. In bad see- ditions. For large N, it can then be shown that the atmospheric ing conditions, this leads to a higher reconstruction error when transfer function associated with the KT average cross-spectrum, using the extended Know-Thompson algorithm and a better per- KT T F( f ) = S i ( f ) S i∗ ( f − δ) i , (3) formance of the speckle masking algorithm. remains ﬁnite up to the diﬀraction limit, D/λ, with D being the telescope pupil diameter. In addition, it is a real entity 2.2. Amplitude reconstruction merely scaling the Fourier amplitudes (Knox & Thompson 1974; The KISIP package reconstructs the object’s Fourier amplitudes von der Lühe 1988). Thus, the extraction of the object’s Fourier using the well-known method of Labeyrie (1970). With phases O( f )/|O( f )| becomes possible from Eq. (2) by use of a recursive or iterative algorithm. The incorporated algorithm ex- |Ii ( f )|2 i = |O( f )|2 |S i ( f )|2 i (6) tends the original idea of Knox and Thompson by using more the object’s spatial power spectrum |O( f )| becomes accessible 2 than two (linear independent) vectors δ. The extension is de- if the speckle transfer function (STF) tailed in von der Lühe (1993), and Mikurda & von der Lühe (2006). S T F( f ) = |S i ( f )|2 i (7) F. Wöger et al.: Speckle interferometry with adaptive optics corrected solar data 377 Fig. 2. Convergence properties of the two implemented algorithms. Upper row: KT algorithm, lower row: IWLS algorithm. Columns from left to right: r0 = 5, 7, 10, 20 cm. Note that a panel of the IWLS algorithm corresponds to a subpanel of a KT panel. Shown is the residual phase variance per pixel in the Fourier domain. is known. Due to the lack of possibility to simultaneously ob- present, there is a need for post-processing the data to achieve the serve a reference point source in the sky when observing the diﬀraction limit of the telescope as often as possible. To achieve sun, the Fourier amplitudes need to be calibrated with model this goal, an analysis has been performed to analyze several im- STFs, the accuracy of which is vital to the photometry of the portant aspects of the KISIP code. ﬁnal reconstruction. In order to chose the correct model func- tion, the value of Fried’s parameter r0 , a measure for the strength of atmospheric turbulence, needs to be well known. When solar 3.1. Code scalability data is reconstructed, the most common way to estimate r0 is The KISIP code has been tested on various combinations of plat- to compute the spectral ratio from the observed data itself. This forms and operating systems, demonstrating its scalability with method was suggested by von der Lühe (1984) and is generally an increasing number of computational nodes and platform in- used by all solar speckle reconstruction algorithms. We have im- dependence. For the tests, we used a data burst with 100 images proved the method for the estimation of r0 originally described consisting of 1024 ×1024 pixels. This data set was reconstructed in von der Lühe (1984) to achieve a higher accuracy especially with either 212 992 cross-spectrum (KT) or 221 320 bispectrum in situations where the spectral ratio is not well deﬁned. A di- (IWLS) values and 30 iterations per 128 × 128 pixel subﬁeld. rect, iterative ﬁt of model spectral ratios to the measured data, We recorded the time to perform the reconstruction using an in- using the squared diﬀerences between model and data as a met- creasing number of computational nodes up to the maximum. ric, increases reliability because more data points are used in the ﬁt. The model functions are precomputed and accessible dur- We present in Fig. 1, the results from tests run on a SuSE ing the process via a lookup table. When an AO system was Enterprise Linux 10 cluster with 23 computational nodes plus used for observations, the models need to be adjusted for the one master node for job administration. This facility is in- AO’s performance and atmospheric anisoplanatism (Wöger & stalled at the Kiepenheuer-Institut für Sonnenphysik. Each of von der Lühe 2007). To correct for anisoplanatism, amplitudes the 24 nodes is equipped with 2 Intel Xeon CPU 5160 with are calibrated separately within each subﬁeld: the spectral ratio 3.00 GHz clock speed and 4 GB of random access memory delivers the appropriate value of r0 and, for AO-corrected data, (RAM). The employed CPUs have 2 cores leading to a total the estimated distance from the AO reference point. The details number of 92 usable processing units – the master node is usu- are described in Wöger & von der Lühe (2007). Using this in- ally not involved in computations. Each computer was connected formation, the photometric properties of the observed object can to the main node via Inﬁniband ﬁbers. As expected, the IWLS be reconstructed to the highest accuracy possible. is slower than the KT algorithm because of the more involved computation. Additionally, Fig. 1 demonstrates that the code be- haves linearly with an increasing number of nodes: the compu- tational time decreases with the inverse of the number of nodes. 3. Reconstruction performance However, there is a saturation in reconstruction time at around We are interested in the possibility of using speckle interferom- 22 s using both algorithms on this platform. etry in real-time applications. Future ground-based solar tele- The saturation is an important issue that needs to be paid scopes will have have apertures of 1.5 m and more (Volkmer close attention to when designing a platform that is supposed et al. 2006; Denker et al. 2006; Wagner et al. 2006) and will to achieve (near) real-time reconstruction performance. The sat- be equipped with AO systems to acquire high-resolution obser- uration is due to latency between the processors, be it because vations. As the correction of an AO system can only be partial of restricted interconnect bandwidth between the computation and its performance is dependent on the atmospheric conditions nodes or because of a slow processor speed. Another reason for 378 F. Wöger et al.: Speckle interferometry with adaptive optics corrected solar data Fig. 3. Top: deconvolved image of the quiet Sun region near disk center observed with Hinode on April 18th, 2007, at 15:30:30 UT. Bottom: the same region observed with the Dunn Solar Telescope (DST); the data was post-processed using KISIP. Images are shown using the same intensity scale. F. Wöger et al.: Speckle interferometry with adaptive optics corrected solar data 379 Fig. 4. Close-up region of the region indicated in Fig. 3. Left: deconvolved Hinode image. Right: reconstructed DST image. Images are shown using the same intensity scale. saturation is the overhead in the code that distributes the data computation. The penalty is longer computational time, as men- to the computation nodes. Thus, an ideal system would pro- tioned before. Nevertheless, greater than 30 iterations (or even vide several multi-core processors that are connected with a less in case of the IWLS algorithm) in combination with ap- fast system bus, which is the current trend in processor devel- proximately 250 000 evaluated cross- or bi-spectrum values for a opment and high-performance computing. Nevertheless, already 128×128 pixel subﬁeld do not lead to a signiﬁcant further change today a system such as the one tested above would provide near in the reconstructed phase, which allows for the minimization of real-time performance for a camera that reads out and stores a computational time by optimizing the reconstruction parameters. 1024 × 1024 pixel frame at an eﬀective rate of 5 frames per sec- This fact is important with respect to real-time reconstruction of ond. speckle data. 3.2. Convergence properties 3.3. Photometric accuracy In addition to the code’s scalability, we analyzed its conver- gence properties with synthetically distorted data cubes, which To test the accuracy of the phase reconstruction, we compare have been aberrated using phase screens that correspond to speckle reconstructed data taken at the DST of the National Solar atmospheric conditions that are similar to values of r0 = Observatory with data observed simultaneously with the SOT 5, 7, 10, 20 cm. The resulting 4 data cubes had 100 images of size instrument on the Hinode satellite. The data were observed at 256 × 256 pixels. They are the same sets as used in the study of 15:30:30 UT on April 18th, 2007, with both facilities using very Mikurda & von der Lühe (2006). We were interested in the num- similar interference ﬁlters of 1 nm FWHM in the Fraunhofer G- ber of cross- and bi-spectrum values as well as iterations needed band at 430.5 nm. A region of quiet solar granulation near Sun for a satisfactory convergence of the iterative phase reconstruc- center was the target of the observations, the Fried parameter tion for a subﬁeld size of 128 × 128 pixels. For each iteration, was estimated to be r0 ≈ 7 cm, corresponding to average seeing. we compute the property The data observed at the DST and at Hinode have been calibrated using standard ﬂatﬁelding procedures. 1 The DST speckle burst was reconstructed using the IWLS κ( j) = (Φ j ( f ) − Φ j−1 ( f ))2 , (8) M algorithm with a subﬁeld size of 128 × 128 pixels, which corre- f sponds to approximately 7 . It is important for the photometric where j represents the jth iteration step and M is the total num- accuracy that the subﬁeld size be chosen based on the size of ber of evaluated frequency points f . The quantity κ( j) measures the isoplanatic patch, or smaller. However, smaller subﬁelds than the squared diﬀerence from the current iteration step from the 128 × 128 pixel subﬁelds are not recommended because numer- previous, which is an indicator for convergence. ical issues during the Fried parameter estimation could arise. Figure 2 shows the results of a detailed analysis of the im- The Hinode image was deconvolved using a point spread plemented algorithms, focusing on the convergence properties function that was computed from the measured aberrations of the in dependence of atmospheric conditions and number of evalu- SOT main mirror (Suematsu et al. 2008). Is addition, a Wiener ated cross- and bispectrum values. As can be seen, for both the ﬁlter was applied, with a noise estimate derived from the power KT and the IWLS algorithms, these parameters are of impor- at frequencies that are higher than the theoretical diﬀraction cut- tance for convergence. With less severe atmospheric conditions, oﬀ frequency. The deconvolution is necessary to make the in- both algorithms converge faster as the signal-to-noise ratio in formation content of the Hinode image comparable to that of the the images increases with increasing values of r0 . Generally, the speckle interferometric reconstruction. It is successful up to 80% KT algorithm seems to converge more slowly than the IWLS of the diﬀraction limit of the telescope. Beyond those spatial fre- algorithm, which is likely the result of the additional informa- quencies, the employed Wiener ﬁlter cuts oﬀ the signal due to a tion that is used in the averaging process of the bispectrum poor signal-to-noise ratio. 380 F. Wöger et al.: Speckle interferometry with adaptive optics corrected solar data Fig. 5. Left: intensity histograms for the Hinode (red) and the DST image (black) as shown in Fig. 3. Right: azimuthally-integrated, spatial-power spectra of the Hinode (red) and the DST image (black). After reduction and alignment of the DST data to that of Another measure for the similarity of images are the “image Hinode, the overall overlap in the images is 912 × 912 pixels, distance” metrics deﬁned in Mikurda & von der Lühe (2006), corresponding to a ﬁeld of view of almost 50 . Figure 3 demon- here restated for convenience. strates that the speckle algorithm is capable of reconstructing the same structures seen by a telescope that is not hampered by at- 1 D2 = (IDST (x) − IHin (x))2 (10) mospheric turbulence. The minor diﬀerences in ﬁne structure of A x the images arise mainly from the fact that the speckle burst of the DST spans approximately 20 s, as opposed to the single ex- and posure of the Hinode satellite. Thus, the data is only in approx- imation simultaneous and some diﬀerences can be attributed to 1 E2 = (IDST (x) − a − bIHin (x))2 , (11) the evolution of the granulation. However, as the spatial corre- A x lation time of the solar granulation is approximately 5 min, the eﬀect is small. where A is the area of the images. We have evaluated the eu- clidean image distance to be D2 = 0.00368925, and E 2 = The photometric diﬀerences in the images are evaluated in 0.00316514. The values of a and b were computed from a lin- several ways. We calculate the contrast of an image I with ear regression analysis of the scatter of reconstructed and Hinode image intensity. Again, the values demonstrate a good agreement of the two images. C I = σI / I , (9) 4. Conclusions where σI is the standard deviation of the mean value I . In the We have presented the KISIP software package, which is capa- speckle reconstructed DST image, this value is CDST = 15.1%, ble of reconstructing solar speckle interferometric data observed which is close to the value CHin = 16.3% in the deconvolved using an AO system. The program is optimized to run in multi- Hinode image. To analyze this further, we computed histograms processor environments to make use of parallel computing capa- of the images’ intensities with a binsize of 0.01 in normalized bilities. While the reconstruction algorithms are based on well- intensity. The histograms, shown in Fig. 5 (left), are very sim- known principles they had to be adapted for use with solar data, ilar and indicate the similarity of the intensity distribution. The e.g., the amplitude calibration and estimation of the Fried pa- diﬀerences can be attributed to certain spatial scales using the ra- rameter r0 . The program scales well with an increasing number dially integrated, spatial power spectra shown for both images in of nodes and shows good convergence properties in every sit- Fig. 5 (right). The abscissa is normalized to the theoretical spa- uation tested. We have shown that using this program, with a tial cutoﬀ of Hinode’s SOT. Both curves show a striking similar- high performance computing cluster, can lead to near real-time ity, demonstrating the accuracy of the amplitude reconstruction reconstruction performance. discussed above. We attribute the deviations noticeable at nor- The reconstruction accuracy has been demonstrated by com- malized frequency 0.5 and above to the reduction of the signal- parison to data observed co-spatially and co-temporally with the to-noise ratio caused by anisoplanatism. While anisoplanatism Hinode satellite. We have presented evidence that not only the has been accounted for in the implemented model transfer func- ﬁne structure in ground-based data can be reconstructed well tions, the signal-to-nose ratio in the ﬁelds furthest away from with this computer program, but also that high photometric accu- the structures that were used as reference for the AO correction racy can be achieved, even when the data that was obtained with (“lock-point”) is lower. This can lead to lower phase reconstruc- an AO system. This has been achieved by implementing new tion performance in those parts of the observed ﬁeld, and thus models for the object’s Fourier amplitude calibration. Satellite reduced contrast contributions from higher spatial frequencies. and ground-based data match very well. F. Wöger et al.: Speckle interferometry with adaptive optics corrected solar data 381 One source for the deviation in contrast could be diﬀerent References amounts of stray light in Hinode/SOT and the DST. This is an Ayers, G. R., Northcott, M. J., & Dainty, J. C. 1988, J. Opt. Soc. Am. A, 5, 963 important issue when comparing contrasts and can lead to sig- Denker, C., Goode, P. R., Ren, D., et al. 2006, in Presented at the Society of niﬁcant biases in both intensity histograms and integrated power Photo-Optical Instrumentation Engineers (SPIE) Conference, Ground-based and Airborne Telescopes, ed. Larry L. M. Stepp Proceedings of the SPIE, spectra, especially when data is compared which was observed 6267, 62670A using two facilities. Due to the lack of information on the stray Denker, C., Yang, G., & Wang, H. 2001, Sol. Phys., 202, 63 light characteristics, we have assumed that the eﬀect is similar Knox, K. T., & Thompson, B. J. 1974, AJ, 193, L45 for both telescopes and have applied no correction. Stray light Labeyrie, A. 1970, A&A, 6, 85 would lead to a constant oﬀset in the power spectra. Accurate Lohmann, A. W., Weigelt, G., & Wirnitzer, B. 1983, Appl. Opt., 22, 4028 Matson, C. L. 1991, J. Opt. Soc. Am. A, 8, 1905 measurements of stray light are needed to compute an accurate Mikurda, K., & von der Lühe, O. 2006, Sol. Phys., 235, 31 contrast for comparison with hydrodynamic models. MPI Forum. 1997, The Message Passing Interface Standard, The anisoplanatism introduced by atmosphere and AO sys- http://www.mpi-forum.org/ tem can make the phase reconstruction performance dependent Pehlemann, E., & von der Lühe, O. 1989, A&A, 216, 337 Suematsu, Y., Tsuneta, S., Ichimoto, K., et al. 2008, Sol. Phys., 26 of the ﬁeld of view and might be another source of diﬀerences van Noort, M., Rouppe van der Voort, L., & Löfdahl, M. G. 2005, Sol. Phys., between the images. This problem could be alleviated in the 228, 191 future by the use of multi-conjugate adaptive optics systems. Volkmer, R., von der Lühe, O., Kneer, F., et al. 2006, in Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, Ground- based and Airborne Telescopes, ed. Larry L. M. Stepp Proceedings of the SPIE, 6267, 62670W von der Lühe, O. 1984, J. Opt. Soc. Am. B Opt. Phys., 1, 510 Acknowledgements. The National Solar Observatory is operated by the von der Lühe, O. 1985, A&A, 150, 229 Association of Universities for Research in Astronomy, Inc. (AURA), under von der Lühe, O. 1988, J. Opt. Soc. Am. A, 5, 721 cooperative agreement with the National Science Foundation. Hinode is a von der Lühe, O. 1993, A&A, 268, 374 Japanese mission developed and launched by ISAS/JAXA, collaborating with Wagner, J., Rimmele, T. R., Keil, S., et al. 2006, in Presented at the Society of NAOJ as a domestic partner, NASA and STFC (UK) as international partners. Photo-Optical Instrumentation Engineers (SPIE) Conference, Ground-based Scientiﬁc operation of the Hinode mission is conducted by the Hinode science and Airborne Telescopes, ed. Larry L. M. Stepp Proceedings of the SPIE, team organized at ISAS/JAXA. This team mainly consists of scientists from in- 6267, 626709 stitutes in the partner countries. Support for the post-launch operation is pro- Weigelt, G. P. 1979, in High Angular Resolution Stellar Interferometry, ed. vided by JAXA and NAOJ (Japan), STFC (UK), NASA (USA), ESA, and NSC J. Davis & W. J. Tango, IAU Colloq., 50, 33–1 (Norway). Wöger, F., & von der Lühe, O. 2007, Appl. Opt., 46, 8015

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 17 |

posted: | 11/5/2011 |

language: | English |

pages: | 7 |

OTHER DOCS BY xiuliliaofz

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.